Answer to Question #131045 in Operations Research for Nokwe

Question

Brian visits Game-on. He is interested in playing two games, that is ‘Rocket league’ and Horizon Chase’. It costs R5,00 to play Rocket league and R2,00 to play Horizon chase. Brian has R20,00 to use in playing games.

Find out if Brian will be able to play 3 games each of Rocket league and Horizon chase. Find all possible combinations of games that Brian can play.

Answer 1

Let $x=$ the number of games of Rocket league, $y=$ the number of games of Horizon chase.

Then

$$5x+2y\leq20$$

If $x=3=y$

$$5x+2y=5(3)+2(3)=21>20$$

Brian will not be able to play 3 games each of Rocket league and Horizon chase.

$x=0: 5(0)+2y\leq20$

$y\leq10$

If Brian does not play Rocket league, he can play at most 10 games of Horizon chase.

$x=1: 5(1)+2y\leq20$

$y\leq7$

If Brian plays 1 game of Rocket league, he can play at most 7 games of Horizon chase.

$x=2: 5(2)+2y\leq20$

$y\leq5$

If Brian plays 2 games of Rocket league, he can play at most 5 games of Horizon chase.

$x=3: 5(3)+2y\leq20$

$y\leq2$

If Brian plays 3 games of Rocket league, he can play at most 2 games of Horizon chase.

$x=4: 5(4)+2y\leq20$

$y=0$

If Brian plays 4 games of Rocket league, he cannot play Horizon chase.

Brain can play at most 10 games of Horizon chase.

Brain can play at most 4 games of Rocket league.